Problem: Nadia is 30 years older than Christopher. Thirteen years ago, Nadia was 4 times as old as Christopher. How old is Christopher now?
Explanation: We can use the given information to write down two equations that describe the ages of Nadia and Christopher. Let Nadia's current age be $n$ and Christopher's current age be $c$ The information in the first sentence can be expressed in the following equation: $n = c + 30$ Thirteen years ago, Nadia was $n - 13$ years old, and Christopher was $c - 13$ years old. The information in the second sentence can be expressed in the following equation: $n - 13 = 4(c - 13)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $c$ , it might be easiest to use our first equation for $n$ and substitute it into our second equation. Our first equation is: $n = c + 30$ . Substituting this into our second equation, we get the equation: $(c + 30)$ $-$ $13 = 4(c - 13)$ which combines the information about $c$ from both of our original equations. Simplifying both sides of this equation, we get: $c + 17 = 4 c - 52$ Solving for $c$ , we get: $3 c = 69$ $c = 23$.